Help With Homework: Power Expansion Confusion

In summary, the conversation is about a student struggling with a review exam for a test. The student is having difficulty understanding how to write a power expansion for a given function and is seeking help. The teachers suggests using the FOIL method, but the student clarifies that they need to come up with a summation. The teacher then explains the process of finding the Taylor's series and using the fact that 1/(1-x) and 1/(1-x^2) can be written as geometric series. The student eventually understands and thanks the teacher for their help.
  • #1
walter9459
20
0

Homework Statement


I am trying to do our the review exam our teacher posted to study for a test and I am having difficulty trying to figure out where to start and what to do. Our teacher lost me when he was explaining this section. Please help!



Homework Equations


Write the power expansion for a given function.

x
-------------
(1-x)(1-x^2)


The Attempt at a Solution

I wasn't sure where to start or what I need to do!
 
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  • #2
did u try F.O.I.L?(first outer inner last) i believe that is all it is asking
 
  • #3
Thanks! But that is not what he is looking for. I need to come up with a summation. One example he worked for us in class was e^(-x^2) = summation (-1)^n [(x^(2n))/n!].
 
  • #4
Since this is in the "Calculus and Beyond" section I would rather interpret that as expanding the function in a power series. One way to do that is to find the Taylor's series for the function. Another way is to use the fact that
[tex]\sum_{n=0}^\infty r^n= \frac{1}{1- r}[/tex]
to interpret 1/(1- x) and 1/(1-x2) as geometric series with r= x and r= x2. Multiply those together (be careful with that) and multiply the result by x (easy).
 
  • #5
Sorry to be so dense but I really have hit a wall where this concept is concerned. I understand what you are saying but not sure what you meant to do next. I really need to understand this concept as I have a test coming up! Thanks!
 
  • #6
Have you written 1/(1-x) and 1/(1- x2) as power series as I said? That is the first step.
 
  • #7
Please accept my apologies. I had been studying all day and had hit a wall. I stepped away and when I came back, it all made sense. Your assistance was greatly appreciated! Thank you for all your help!
 

1. What is meant by "power expansion confusion"?

Power expansion confusion refers to the difficulty in understanding and applying the concept of power expansion in mathematical equations. This involves expanding equations using the power rule, which can be complex and confusing for some individuals.

2. How can I improve my understanding of power expansion?

Practice is key when it comes to understanding power expansion. It is important to start with simple equations and gradually work your way up to more complex ones. You can also seek help from a tutor or use online resources for additional practice and clarification.

3. What are some common mistakes to avoid when using power expansion?

One common mistake is forgetting to apply the power rule when expanding equations. It is also important to correctly identify the base and exponent in the equation. Another mistake is not simplifying the expanded equation, which can lead to incorrect solutions.

4. Are there any tips or tricks for mastering power expansion?

One helpful tip is to break down the equation into smaller parts and apply the power rule to each part individually. It is also important to memorize common powers, such as (x^2)^2 = x^4, to make the process easier. Practice and repetition are also key in mastering power expansion.

5. How can I use power expansion in real-life situations?

Power expansion is commonly used in physics and engineering to model and solve various problems. It is also used in economics, finance, and other fields that involve complex mathematical equations. Understanding power expansion can also help in simplifying and solving everyday problems involving exponents.

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